**SURFACE AREA AND VOLUME OF COMBINATIONS**

**Cone on a Cylinder.**

r = radius of cone & cylinder;

h_{1} = height of cone

h_{2} = height of cylinder

Total Surface area = Curved surface area of cone + Curved surface area of cylinder + area of circular base

= πrl + 2πrh_{2} +πr^{2};

Slant height, l =

Total Volume = Volume of cone + Volume of cylinder

=

**Cone on a Hemisphere:**

h = height of cone;

l = slant height of cone =

r = radius of cone and hemisphere

Total Surface area = Curved surface area of cone + Curved surface area of hemisphere = πrl + 2πr^{2}

Volume = Volume of cone + Volume of hemisphere =

**Conical Cavity in a Cylinder**

r = radius of cone and cylinder;

h = height of cylinder and conical cavity;

l = Slant height

Total Surface area = Curved surface area of cylinder + Area of bottom face of cylinder + Curved surface area of cone = 2πrh + πr^{2} + πrl

Volume = Volume of cylinder – Volume of cone =

**Cones on Either Side of Cylinder.**

r = radius of cylinder and cone;

h_{1} = height of cylinder

h_{2} = height of cones

Slant height of cone, l =

Surface area = Curved surface area of 2 cones + Curved surface area of cylinder = 2πrl + 2πrh_{1}

Volume = 2(Volume of cone) + Volume of cylinder =

**Cylinder with Hemispherical Ends.**

r = radius of cylinder and hemispherical ends;

h = height of cylinder

Total surface area= Curved surface area of cylinder + Curved surface area of 2 hemispheres = 2πrh + 4πr^{2}

Volume = Volume of cylinder + Volume of 2 hemispheres =

**Hemisphere on Cube or Hemispherical Cavity on Cube**

a = side of cube;

r = radius of hemisphere.

Surface area = Surface area of cube – Area of hemisphere face + Curved surface area of hemisphere

= 6a^{2} – πr^{2} + 2πr^{2} = 6a^{2} + πr^{2}

Volume = Volume of cube + Volume of hemisphere =

**Hemispherical Cavity in a Cylinder**

r = radius of hemisphere;

h = height of cylinder

Total surface area = Curved surface area of cylinder + Surface area of base + Curved surface area of hemisphere

= 2πrh + πr^{2} + 2πr^{2} = 2πrh + 3πr^{2}

Volume = Volume of cylinder – Volume of hemisphere =